Communication of information between computers and other electronic devices can be implemented using any of a variety of different standards and technologies. Channel coding and error correction techniques can be used to reduce errors in received signals introduced from distortion and other disturbances. Such coding and error correction can be implemented using an encoder and a decoder at the ends of the transmission channel.
One increasingly popular communication standard is 10 Gigabit Ethernet, with a nominal data rate of 10 Gbit/s. One standard of 10 Gigabit Ethernet is IEEE 10 GBASE-T, used to provide 10 gigabit per second connections over unshielded or shielded twisted pair cables. The wire-level modulation for 10 GBASE-T is a Tomlinson-Harashima Precoded (THP) version of pulse-amplitude modulation with 16 discrete levels (PAM-16), encoded in a two-dimensional constellation pattern known as 128-DSQ (Double Square QAM).
As shown in FIG. 1, the 10 GBASE-T transmission frame is based on a (2048, 1723) Low Density Parity Check (LDPC) code, i.e. 2048 total bits with 1723 data bits and 325 check bits per frame, where the check bits are used to fix or detect errors in the frame. This is used in combination with the 128-DSQ synthetic constellation that uses a combination of coded and uncoded bits to transmit information. As shown, Ethernet data is retrieved in fifty 65-bit blocks and is scrambled, e.g. provided to a self-synchronizing scrambler to scramble the bits, and a CRC-8 generation of 8 check bits is provided on one end of the frame and an auxiliary channel bit on the other end, creating 3259 bits in the frame payload. The payload is then divided up into 1723 bits for the LDPC coder, and 1536 uncoded bits (3×512) that are not coded by the LDPC coder. The coded LDPC check bits (325 bits) are added to the end of the payload. The LDPC block size after coding is 2048 total bits (4×512).
The resulting frame is mapped to 128-DSQ symbols, and the resulting DSQ symbols are then precoded using THP. Each of these 512 128-DSQ symbols are then transmitted as a pair of PAM-16 symbols (x-axis and y-axis), to create 1024 symbols (3584 bits). The constellation for 128-DSQ symbols is shown in FIG. 2, and consists of 8 cosets (regions), each coset containing 16 points. The coset label contains the 3 uncoded bits as shown in FIG. 2, and the points within the coset contain the 4 coded bits protected using the LDPC block code. The labeling of the points in the coset (the coset elements) conveying the 4 coded bits is shown in FIG. 3.
The receiver unscrambles a received frame and decodes the coded bits. Any of several decoding algorithms for LDPC codes can be used in the receiver to decode the received coded bits. For example, iterative decoders are often used to converge on a correct decoded value. In one implementation, LDPC decoding is performed in the receiver using a soft-decision, message-passing algorithm. The bits are treated as continuous variables which represent the probability of the value being a 0 or a 1, and the continuous variables are represented in the decoding algorithm as Log Likelihood Ratios (LLRs). The message passing algorithm sets the variable nodes to the soft receive LLRs, calculates the syndrome LLRs given the variable LLRs, updates the variable LLRs with the new syndrome information, and iterates in this same way until a convergence is reached (e.g., check bits are zero). Using the 10 GBASE-T transmission scheme, it is possible to have very low bit error rates that come very close to the Shannon limit of the communication channel.
However, one of the problems that is inherent to LDPC codes is the presence of trapping sets. A trapping set is the set of data nodes (bits) that cannot always be decoded to the correct value after any given number of iterations. These are stable solutions to the LDPC decoding problem that typically manifest themselves in a cluster of interconnected nodes, such that the influence from outside these nodes is limited, i.e. they are a set of variable nodes not well-connected to the rest of the graph and causing a failure in decoding. Thus, during the decoding operation it is possible to get “stuck” in a trapping set, as opposed to converging to the correct solution, causing the decoding operation to fail and setting the ultimate error floor of the decoding process. There have been attempts to bias the decoding process to avoid trapping sets, but when encountered, the trapping sets cause the decoding to fail. Failed decoding of the frame leads to undesired retransmission of the frame or undesired noise at the receiver.
Accordingly, what is needed is a system and method that addresses decoding issues of trapping sets.